Mass Defect

Outcomes You will relate, qualitatively and quantitatively, the mass defect of the nucleus to the energy released in nuclear reactions, using Einstein’s concept of mass-energy equivalence

Nuclear Binding Energy The energy required to separate the nucleons of a nucleus (can be equated to the strong forces holding the nucleus together) Binding energy: the energy required to separate all of a nuclei’s protons and neutrons infinitely far apart Binding energy = energy of (individual) nucleons – energy of nucleus Eb = Enucleons - Enucleus

Mass Defect The assembled nucleus is ALWAYS lighter than the parts that make it up TWO WAYS TO THINKS OF THIS… The energy added to the nucleus to separate the nucleons shows up as mass Some of the mass of the nucleons is released as energy when they bind to make the nucleus

Einstein and Binding Energy Einstein’s formula E=mc2 states that mass and energy are equivalent Whenever the nucleus undergoes some change, mass converts into energy and the mass converted is known as the mass defect Conservation of energy still applies: the energy of the individual nucleons is equal to the sum of the energy of the nucleus and binding energy, leading us to: Eb = Enucleons – Enucleus

Calculations Mass Defect mass defect = mass of the nucleons – mass of the assembled nucleus. m = [N(1.6749x10-27) +Z(1.6726x10-27)] – (A)(u) Where N = # of neutrons and Z = # of protons (predicted) Where, A=atomic mass number (total number of nucleons) and u =1.66x10-27kg (actual) Binding Energy Energy = mass defect x speed of light squared E=mc2

Sample Problem The mass of a helium nucleus is 6.6443 x 10-27 kg ( 4 2 He). What is the mass defect and binding energy of the helium nucleus? (Use the following for proton and neutron masses: proton = 1.6726 x 10-27 kg and neutron = 1.6749 x 10-27 kg)

Half-Life

Outcomes You will perform simple, non-logarithmic half-life calculations

Radioactivity The rate that a radioactive sample transmutes can be expressed by either its activity or its half-life Half-life: is the time it takes one half of a radioactive sample to decay Activity: the number of nuclei that change in a given period of time. The standard SI unit for the activity is the Becquerel: 1Bq = 1decay/s

Graphing What is the half-life of this particular material?

Half-life Calculations THIS PART OF THE FORMULA IS NOT ON YOUR FORMULA SHEET!

Sample Problem The half life of iodine-131 is 8.040 days. What percentage of an iodine-131 sample will remain after 40.20 days?

Homework Mass Defect and Half-life p. 182 #1-4 Calculation Questions: p. 817 #5 & 7 and p. 184 #1-5 Graph Question: p. 817 #8